US20110234432A1 - Systems and methods for optimizing bit utilization in data encoding - Google Patents

Abstract

In one of many possible embodiments, a system for optimizing bit utilization in data encoding is provided. The exemplary system includes a data processing subsystem configured to identify a total number of unique characters within a set of data, which number represents an original base of representation of the set of data. The data processing subsystem is further configured to convert the set of data to a base of representation that is higher than the original base of representation and then encode the base-converted data with a fixed-length encoding scheme.

Description

RELATED APPLICATION
• This application is a continuation of, and claims priority to, co-pending application Ser. No. 11/474,990, filed Jun. 27, 2006, and entitled “SYSTEMS AND METHODS FOR OPTIMIZING BIT UTILIZATION IN DATA ENCODING,” the contents of which are hereby incorporated herein by reference in their entirety.
BACKGROUND INFORMATION
• The advent of computers, interactive electronic communication, the Internet, and other advances in the digital realm of consumer electronics have resulted in a need for digital data encoding techniques that are accurate and efficient.
• Fixed length encoding is one type of data encoding technique that is commonly used to store and transmit digital data. In fixed length encoding, a number of digital bit patterns of fixed lengths are used to define the characters or symbols of a written language, thus allowing digital devices to store, process, and communicate character-oriented information.
• Common fixed length encoding schemes include, but are not limited to, the American Standard Code for Information Interchange (ASCII), extended-ASCII, Extended Binary-Coded Decimal Interchange Code (EBCDIC), and Unicode. In ASCII, for example, a seven bit encoding scheme is used to represent ninety-four printable characters including letters, numbers, and punctuation symbols in addition to thirty-four control characters and other “special characters.” In extended-ASCII, an eighth bit is added to the encoding scheme to facilitate representation of 128 additional symbols.
• Fixed length encoding is used to store and transmit all types of data. For example, fixed length encoding is often used to store and transmit large compilations of text and/or numbers, such as names, telephone numbers, credit card numbers, social security numbers, and other identification numbers.
• However, fixed length encoding is inherently inefficient when used to encode certain types of data. For example, when decimal data (i.e., data that includes the digits between 0 and 9) is stored using extended-ASCII encoding, fifty percent or more of the consumed storage medium may be wasted on bits that are not necessary to represent the data. Moreover, the encoding of large data files often requires large storage media and time-consuming data processing.
BRIEF DESCRIPTION OF THE DRAWINGS
• The accompanying drawings illustrate various embodiments and are a part of the specification. The illustrated embodiments are merely examples and do not limit the scope of the disclosure. Throughout the drawings, identical reference numbers designate identical or similar elements.
• FIG. 1 illustrates an example of an encoding system, according to an embodiment.
• FIG. 2 illustrates an example of an encoding system further configured to decode encoded data, according to an embodiment.
• FIG. 3 illustrates the contents of an exemplary digit list file corresponding to a particular set of data, according to an embodiment.
• FIG. 4 illustrates an exemplary method of encoding a set of data in a fixed length encoding scheme, according to an embodiment.
• FIG. 5 illustrates an exemplary method of decoding data that has been base-converted and encoded, according to an embodiment.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTSI. Introduction
• Systems and methods for optimizing bit utilization in data encoding are described herein. A set of data that is to be encoded is first analyzed to identify the total number of unique characters contained therein. The total number of unique characters may then be designated as an original base of representation of the set of data. The set of data is then converted to a base of representation that is higher than the original base of representation. The base-converted data may then be encoded with any suitable fixed-length encoding scheme.
• In certain embodiments, by converting the set of data to a higher base of representation prior to encoding, the systems and methods described herein optimize bit utilization by reducing the number of characters that are encoded. In some examples, the higher base of representation may be chosen to optimize the bit utilization of the encoding system. For example, the set of data may be converted into a base of representation that is the highest power of the original base of representation permitted by the length of the particular encoding scheme.
• To facilitate an understanding of the systems and methods described herein, a number of terms related to number systems, fixed length encoding, and bit utilization will now be described.
A. Number Systems
• As used herein, the term “number system” will be used to refer to a set of rules used to map a numeral to a number. A “number” is an ideal or conceptual quantitative value. A “numeral” is a symbol used to visually represent a number. For example, in certain number systems the numerals 1 and 0.999 both represent the same number, one.
• The “base” or “radix” of a particular number system refers to the quantity of digits, including zero, that the number system uses to represent a number. For example, the decimal number system, one of the most commonly used number systems, has a base of representation equal to 10. Hence, the maximum number a single digit in the decimal number system will ever reach is 9, after which it becomes necessary to add another digit to represent a higher number.
• An n digit decimal number is represented by the equation given in Equation 1.
• $\begin{array}{cc}\sum _{i=0}^{n-1}d_i{10}^i& \mathrm{Equation}1\end{array}$
• The variable d_ishown in Equation 1 represents each digit in the n digit decimal number. For example, the number “1234” includes four digits—d₀is 4, d₁is 3, d₂is 2, and d₃is 1.
• Equation 1 may be generalized to represent an n digit number in any number system. In general, an n digit number in a number system of base B may be represented by the equation given in Equation 2.
• $\begin{array}{cc}\sum _{i=0}^{n-1}d_iB^i& \mathrm{Equation}2\end{array}$
• As the base of representation increases, the number of digits needed to represent a particular number decreases. For example, three digits are required to represent the number “seven” in binary, or base 2. However, in decimal, or base 10, only one digit is needed to represent the number “seven.” Equation 3 shows a formula that may be used to calculate the number of digits needed to represent a number N with radix r:
• 
  ┌log_r(N+1)┐  Equation 3
• A number may be represented using any number system as may serve a particular application. Moreover, a number may be converted from one base of representation to another (e.g., from binary to decimal or vice versa). In some examples, conversion from one base of representation to another may be performed by using one of a number of different algorithms and/or look-up tables.
B. Fixed Length Encoding
• Fixed length encoding is a method of representing characters or symbols in a way that can be manipulated by a digital device, such as a computer. In fixed length encoding, a number of bits are first grouped into elements of a specified size. Each permutation of the bits may then be mapped to represent a single character. In this manner, each character may be stored, processed, and/or transmitted by a digital device. As used herein, the “length” of a particular fixed-length encoding scheme refers to the number of bits used within that encoding scheme to represent a single character. For example, an 8-bit encoding scheme has a length of 8.
• As mentioned, common fixed length encoding schemes include, but are not limited to, the American Standard Code for Information Interchange (ASCII), extended-ASCII, Extended Binary-Coded Decimal Interchange Code (EBCDIC), and Unicode. Each of these encoding schemes will be described in more detail below. However, it will be recognized that fixed length encoding is in no way limited to the encoding schemes described herein.
• 1. ASCII
• ASCII encoding is pervasive in the computing industry and is the data encoding scheme of choice for many computing platforms and network transmissions. In ASCII encoding, groups of seven bits are used to represent 94 printable characters in addition to 34 control characters and other “special characters.” Basic ASCII is typically augmented by extended-ASCII, in which an eighth bit is used to facilitate representation of 128 additional symbols. As used herein and in the appended claims, unless otherwise specifically denoted, the term “ASCII” is defined broadly to include extended-ASCII.
• 2. EBCDIC
• EBCDIC is an 8-bit encoding scheme currently used in some types of applications including, but not limited to, various IBM platforms. However, most IBM platforms and other applications that use EBCDIC are configured to convert EBCDIC to ASCII or Unicode when required.
• 3. Unicode
• Unicode is a fixed length encoding scheme that has recently been developed in an effort to replace existing encoding schemes that are limited in size and incompatible with multilingual environments. Unicode encoding includes three major specifications: UTF-8, UTF-16, and UTF-32. UTF stands for Unicode Transformation Format.
• UTF-8 is a variable length grouping of 1 through 4 bytes, each encoded in 8 bits. UTF-8 is commonly used in Hypertext Markup Language (HTML) and has the advantage that bit combinations for the standard ASCII characters are represented by the same bit combinations in UTF-8.
• UTF-16 encodes commonly used characters in 16 bits. Other characters are also available in UTF-16 encoding by adding a second 16-bit byte. UTF-16 balances storage with efficient access to characters. UTF-32 is a 32-bit encoding scheme that is used to provide a unique single code for each character in a given language or application.
• Unicode has been implemented in many recent technologies, including, but not limited to, extensible markup language (“XML”), Java, and modern operating systems.
C. Bit Utilization
• As will be described in more detail below, the particular number system used in any fixed length encoding scheme affects the bit utilization of an encoded set of data. As used herein, the term “bit utilization” (“BU”) is defined as the ratio of bits containing number system related information divided by total number of bits used by the encoding scheme. For example, if an 8-bit encoding scheme is used to encode a decimal7 as “00000111”, only three of the eight bits contain number system related information. Hence, the bit utilization is ⅜ or 37.5 percent.
• The average bit utilization BU_avefor data represented by a base B number system and stored using fixed length encoding can be expressed as shown in Equation 4.
• 
  BU_{ave [B,n]}=(i+2−(2ⁱ⁺¹/B))/jn  Equation 4
• In Equation 4, the variable B represents the base or radix of the number system. The variable i represents the exponent of the highest power of 2 where 2ⁱ≦B. The variable n represents the number of bits in one storage container (e.g., if one set or storage container of 8 bits is used to represent a digit, n is equal to 8). The variable j represents the smallest integer such that 2^jn≧B.
• The average bit utilization equation shown in Equation 4 describes the relationship between the base of representation and the bit utilization of the particular encoding scheme that is used to encode a set of data. In general, as the base of representation increases, the average bit utilization also increases. Hence, in some examples, the base of representation of a particular set of data may be converted to a higher base of representation in order to improve the bit utilization of the system used to encode the data.
• To illustrate the concept of average bit utilization, Equation 4 will be used to derive the average bit utilization of decimal (base 10) data. In the following illustration, it is assumed that 8-bit encoding is used to encode the data. For decimal data, the parameters for Equation 4 include the following:
• The variable B is 10 because the base of representation of decimal data is 10.
• The variable i is 3 because 3 is the exponent of the highest power of 2 such that 2ⁱ≦10.
• The variable n is 8 because the encoding scheme uses 8 bits to represent each digit within the data.
• The variable j is 1 because 1 is the smallest integer such that 2^jn≧10.
• By inserting the parameters listed above into the average bit utilization equation shown in Equation 4, it can be shown that BU_{ave [10,8]}=(3+2−2⁴/10)/(1*8)=3.4/8=0.425. Hence, the average bit utilization for decimal data encoded using an 8-bit encoding scheme is 42.5 percent.
• The derivation of the average bit utilization for decimal data using 8-bit encoding may be more fully understood by analyzing the actual bits used to encode the digits that are included in a decimal number system. Table 1 illustrates an exemplary 8-bit encoding scheme that may be used to encode each of thedigits 0 through 9 that are included in a decimal number system.

• 	TABLE 1
  	Digit	Encoding Representation
  	0	00000000
  	1	00000001
  	2	00000010
  	3	00000011
  	4	00000100
  	5	00000101
  	6	00000110
  	7	00000111
  	8	00001000
  	9	00001001

• For ease of explanation, the bits shown in Table 1 will be interchangeably referred to herein as “bit0” (right-most bit) through “bit7” (left-most bit) or as the “first bit” (right-most bit) through the “eighth bit” (left-most bit).
• As shown in Table 1, if only bit0 of an encoded digit is known, the encoded digit could be any one of 5 digits. For example, if it is known thatbit0 is “0”, the encoded digit could be 0, 2, 4, 6, or 8. Alternatively, if it is known thatbit0 is “1”, the encoded digit could be 1, 3, 5, 7, or 9.
• However, ifbits0 and1 are known, the encoded digit could be one of either 2 or 3 digits. For example, ifbits0 and1 are both “0”, the encoded digit could be 0, 4, or 8.
• Ifbits0 through2 are known, it is possible to determine the value of the encoded digit if the three bit sequence is anything other than “000” or “001.” This is becausedigits 0 and 8 end in “000” and digits 1 and 9 end in “001”.
• Finally, ifbits0 through3 are known, the value of any encoded digit may be determined because all ten encoding representations have unique bit patterns forbits0 through3.
• Hence, if the encoded digit is 2, 3, 4, 5, 6, or 7, only three total bits are required to determine the value of the encoded digit. However, if the encoded digit is 0, 1, 8, or 9, all four bits are required to determine the value of the encoded bit. In other words, all of the digits fully utilize the first three bits, while four out of the ten digits utilize the fourth bit. Hence, even though all eight bits are used to represent each digit, only 3+(4/10) of them on average contain number system related information. Therefore, the average bit utilization of a decimal number system encoded with an 8-bit encoding scheme is (3+(4/10))/8=0.425 or 42.5 percent.
• To illustrate the effect of a change in base of representation on the average bit utilization of a system used to encode a set of data, the average bit utilization equation shown in Equation 4 will now be used to derive the average bit utilization of base 26 data. For base 26 data, the parameters for Equation 4 include the following:
• The variable B is 26 because the base of representation of the data is 26.
• The variable i is 4 because 4 is the exponent of the highest power of 2 such that 2ⁱ≦26.
• The variable n is 8 because the encoding scheme uses 8 bits to represent each digit within the data.
• The variable j is 1 because 1 is the smallest integer such that 2^jn≧26.
• By inserting the parameters listed above into the average bit utilization equation shown in Equation 4, it can be shown that BU_{ave [26,8]}=(4+2−2⁵/26)/(1*8)≈4.7692/8≈0.5962. Hence, the average bit utilization for base 26 data encoded using an 8-bit encoding scheme is about 59.6 percent.
• A useful metric for comparing bit utilization values of two different number systems is given in Equation 5.
• 
  rBU_{[B1,B2,n1,n2]}=BU_[B1,n1]=BU_[B2,n2]  Equation 5
• As shown in Equation 5, the relative bit utilization rBU when converting from base B1 with n1 bit representation to base B2 with n2 bit representation may be calculated by dividing the bit utilization of the first number system (B1) by the bit utilization of the second number system (B2). For example, using the average bit utilization values derived previously for base 10 and for base 26, it can be seen that the base 10 bit utilization is about 71 percent as efficient as the base 26 bit utilization (0.425/0.5962≈0.71).
• As mentioned, the formula given in Equation 4 may be used to calculate the average bit utilization of a set of data represented by any base B number system. Formulas may also be derived to calculate best and worst case bit utilization values. For example, Equation 6 shows a formula that may be used to calculate the best case bit utilization BU_bestand Equation 7 shows a formula that may be used to calculate the worst case bit utilization BU_worst.
• 
  BU_{best [B,n]}=(i+1)/jn  Equation 6
• 
  BU_worst[B,n]=i/jn  Equation 7
• The variables used in Equations 6-7 are the same as those used and described in connection with Equation 4. Using Equation 6, it can be shown that the best case bit utilization of 8-bit encoding of base 10 data is 50 percent. Likewise, using Equation 7, it can be shown that the worst case bit utilization of 8-bit encoding of base 10 data is 37.5 percent.
• The expected best case, average case, and worst case bit utilization values for 8-bit ASCII encoding are listed in Table 2 for a number of different bases of representation. The bases of representation shown in Table 2 are merely illustrative. The expected best case, average case, and worst case bit utilization values for any other base of representation may be derived using the equations shown above.

• TABLE 2
  Base of Number	Best Case Bit	Average Case Bit	Worst Case Bit
  System	Utilization	Utilization	Utilization

  2	0.125	0.125	0.125
  4	0.25	0.25	0.25
  8	0.375	0.375	0.375
  10	0.5	0.425	0.375
  16	0.5	0.5	0.5
  32	0.625	0.625	0.625
  50	0.75	0.715	0.625
  100	0.875	0.84	0.75
  256	1.0	1.0	1.0

• As illustrated in Table 2, the expected best case, average case, and worst case bit utilization values for 8-bit ASCII encoding increase as the base of representation of the number system increases.
D. Exemplary Implementations
• The systems and methods described herein may be used to improve the bit utilization of any fixed length encoding scheme and may be used in connection with many different types of data processing. For example, the systems and methods described herein may be used to improve bit utilization in data storage, data compression, data manipulation and sorting, infinite length integer representation, and data transmission. It will be recognized that the systems and methods described herein may additionally or alternatively be used to improve bit utilization in any other type of data processing.
• For example, the systems and methods described herein may serve to reduce the amount of space needed to store certain types of data in non-volatile storage devices (e.g., local hard drives and network drives). Moreover, the systems and methods described herein may serve to improve overall system performance by reducing the amount of input and output operations between internal memory and such non-volatile storage devices.
• To illustrate, typical access times for many non-volatile storage devices can be 10⁻³seconds (milliseconds). However, typical internal memory access times are 10⁻⁹seconds (nanoseconds) for reading from cache and tens of nanoseconds for reading from dynamic random access memory (“DRAM”). Thus, in many examples, it takes at least 100,000 times as long to access data in a non-volatile storage device as it does to access data in internal memory. Hence, even though additional internal memory access operations may be needed to perform the systems and methods described herein, overall system performance may be enhanced by the reduction in the amount of input and output operations between internal memory and non-volatile storage devices.
II. Exemplary System View
• FIG. 1 illustrates an exemplary encoding system100 (or simply “system100”), according to one embodiment. As shown inFIG. 1, adata source101 is configured to providedata102 to adata processing subsystem110.Data source101 anddata processing subsystem110 may communicate using any known communication technologies, devices, media, and protocols supportive of data communications, including, but not limited to, coaxial cables, copper wires, fiber optics, data buses, the Internet, intranets, local area networks, other communications networks, data transmission media, communications devices, Transmission Control Protocol (“TCP”), Internet Protocol (“IP”), File Transfer Protocol (“FTP”), telnet, Hypertext Transfer Protocol (“HTTP”), socket connections, Ethernet, and other suitable communications technologies.
• It has been discovered that overall bit utilization of theencoding system100 increases as the base of representation of the data being encoded by thedata processing subsystem110 increases. Hence, in certain embodiments, thedata processing subsystem110 is configured to optimize bit utilization by converting thedata102 to a higher base of representation before the data is encoded. In this manner, the number of digits that are encoded by thedata processing subsystem110 is decreased, thereby decreasing the total number of bits that have to be used to encode thedata102.
• While anexemplary encoding system100 is shown inFIG. 1, the exemplary components illustrated inFIG. 1 are not intended to be limiting. Indeed, alternative combinations of hardware, software, and/or firmware and implementations thereof may be used, as is well known. Each of the components ofsystem100 will now be described in additional detail.
A. Data Source
• Data source101 may include any device, program, or function configured to generate, store, and/or communicatedata102 to thedata processing subsystem110. For example,data source101 may include a hard drive or database configured to storedata102.
B. Data
• Data102 may include any combination of characters such as, but not limited to, letters, numbers, and symbols. For example, thedata102 may include text in any language, compilations of numbers (e.g., telephone numbers, social security numbers, etc.), or any other combination of characters. Exemplary sets ofdata102 that will be used to illustrate the systems and methods described herein include a database of telephone numbers and a file containing the text of the King James version of the Bible. In some examples, thedata102 is included within a computer readable file, such as a text file.
• As used herein, the term “set of data” or “data set” will be used interchangeably to refer to a designated group of characters that may be encoded.
D. Data Processing Subsystem
• Data processing subsystem110 may include any component or combination of components configured to process thedata102 provided by thedata source101. For example, as shown inFIG. 1, thedata processing subsystem110 may include aprocessor111,base converter112,encoder113,compression module114,non-volatile storage unit115, and/ormemory116.
• In many embodiments, thedata processing subsystem110 is implemented in one or more computers. Thedata processing subsystem110 may include any computer hardware and/or instructions (e.g., software programs), or combinations of software and hardware, configured to perform the processes described herein. In particular, it should be understood thatdata processing subsystem110 may be implemented on one physical computing device or may be implemented on more than one physical computing device. Accordingly,data processing subsystem110 may include any one of a number of well-known computing devices, and may employ any of a number of well-known computer operating systems, including, but by no means limited to, known versions and/or varieties of the Microsoft Windows® operating system, the Unix operating system, the Macintosh® operating system, and the Linux operating system.
• Accordingly, the various processes described herein may be implemented at least in part as instructions executable by one or more computing devices, as is well known. In general, a processor (e.g., a microprocessor) receives instructions, e.g., from a memory, a computer-readable medium, etc., and executes those instructions, thereby performing one or more processes, including one or more of the processes described herein. Such instructions may be stored and transmitted using a variety of known computer-readable media.
• A computer-readable medium (also referred to as a processor-readable medium) includes any medium that participates in providing data (e.g., instructions) that may be read by a computer (e.g., by a processor of a computer). Such a medium may take many forms, including, but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media may include, for example, optical or magnetic disks and other persistent memory. Volatile media may include, for example, dynamic random access memory (“DRAM”), which typically constitutes a main memory. Transmission media may include, for example, coaxial cables, copper wire and fiber optics, including the wires that comprise a system bus coupled to a processor of a computer. Transmission media may include or convey acoustic waves, light waves, and electromagnetic emissions, such as those generated during radio frequency (“RF”) and infrared (“IR”) data communications. Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, an EPROM, a FLASH-EEPROM, any other memory chip or cartridge, or any other medium from which a computer can read.
• While an exemplarydata processing subsystem110 is shown inFIG. 1, the exemplary components illustrated inFIG. 1 are not intended to be limiting. Indeed, additional or alternative components and/or implementations may be used, as is well known. Various components of thedata processing subsystem110 will now be described in additional detail.
• 1. Processor
• As shown inFIG. 1, theprocessor111 is configured to receive andprocess data102 from thedata source101. Theprocessor111 may include any combination of hardware, software, and firmware as may serve a particular application. For example, theprocessor111 may include a central processing unit (CPU), application specific integrated circuit (ASIC), field programmable gate array (FPGA), or any other type of processing circuit.
• In some embodiments, theprocessor111 is configured to parse thedata102 and find and count unique characters contained therein. For example, if thedata102 were to include a compilation of telephone numbers, theprocessor111 may find up to 10 unique characters (0-9) contained therein. Likewise, if thedata102 were to include text from, for example, the King James version of the Bible, theprocessor111 would find87 unique characters contained therein.
• In some examples, theprocessor111 may be further configured to store each of the unique characters within a digit list file that may be located within either thememory116 ornon-volatile storage unit115. It will be recognized that the digit list file may additionally or alternatively be located in any other storage medium as may serve a particular application. The digit list file, as will be described in more detail below, includes a listing of all the unique characters as identified by theprocessor111 within a set ofdata102.
• 2. Base Converter
• Base converter112 is configured to convert a set ofdata102 from a first base of representation to a second higher base of representation. The converted data is represented inFIG. 1 by base-converteddata117. For example, if thedata102 were to include a compilation of decimal digits (e.g., telephone numbers), thebase converter112 may be configured to convert thedata102 into data represented by a higher base number system (e.g., a base 100 number system).
• Thebase converter112 may include any combination of hardware, software, and/or firmware as may serve a particular application. For example, thebase converter112 may include any type of processor, program, and/or combination thereof. In some examples, thebase converter112 uses one or more look-up tables and/or is configured to perform one or more mathematical operations in order to convert thedata102 from one base of representation to another.
• In certain embodiments, thebase converter112 may additionally be configured to convert the base-converteddata117 back intodata102 represented by the first base. In this manner, thedata102 may be accessed at a later time by a user of thedata processing subsystem110.
• 3. Encoder
• Encoder113 may be configured to encode the base-converteddata117 and output encodeddata118. In some examples, theencoder113 may perform any type of fixed length encoding as may serve a particular application. For example, theencoder113 may be configured to encode the base-converteddata117 using ASCII, EBCDIC, and/or Unicode. Moreover, theencoder113 may include any combination of hardware, software, and/or firmware as may serve a particular application.
• The number of bits used in the fixed length encoding may vary as may serve a particular application. For illustrative purposes only, it will be assumed in the examples given herein that 8-bit encoding is used by theencoder113 to encode the base-converteddata117.
• 4. Compression Module
• In some examples, thedata processing subsystem110 may include acompression module114 configured to compress the encodeddata118. Compression is desirable in applications such as data transmission and storage. However, it will be recognized that, in some applications, it is not desirable to compress the encodeddata118.
• Thecompression module114 may include any combination of hardware, software, and/or firmware as may serve a particular application. For example, thecompression module115 may include a known compression utility such as, but not limited to, “zip,” “compress,” “pack,” “gzip,” and “bzip2.”However, it will be recognized that thecompression module114 may additionally or alternatively include any other type of compression utility.
• 5. Non-Volatile Storage Unit
• Non-volatile storage unit115 may include one or more data storage mediums, devices, or configurations and may employ any type, form, and combination of storage media including, but not limited to, hard disk drives, read-only memory, databases, and optical media.Non-volatile storage unit115 may include any known technologies useful for storing, updating, modifying, accessing, retrieving, and deleting data.
• 6. Memory
• Thedata processing subsystem110 may also includememory116.Memory116 may include, but is not limited to, FLASH memory, random access memory (RAM), dynamic RAM (DRAM), one or more buffers, or a combination thereof. Thememory116 may facilitate the temporary storage and/or manipulation ofdata102.
• 7. Additional Components
• In certain embodiments, thedata processing subsystem110 may include any of a number of additional or alternative components. For example, as shown inFIG. 2, thedata processing subsystem110 may include adecoder120 configured to decode the encodeddata118. Thedecoder120 may be configured to convert the encodeddata118 from machine-readable bits back to the base-converteddata117. Thebase converter112 may then convert the base-converteddata117 into theoriginal data102. In addition, thedata processing subsystem110 may include adecompression module121 configured to decompress data that has been compressed by thecompression module114.
• In some examples, one ormore access devices122 may be configured to communicate with thedata processing subsystem110. Theaccess device122 may include any of a number of different types of devices such as, but not limited to, a personal computer, a handheld device (e.g., a personal digital assistant (“PDA”) or a cellular telephone), or any other type of computing device. In some examples, a user may access thedata102 via theaccess device122.
E. Digit List File
• As mentioned, theprocessor111 may be configured to locate and store each of the unique characters within a set ofdata102 in a digit list file. The digit list file may be stored in thenon-volatile storage unit115,memory116, or in any other suitable location.
• FIG. 3 illustrates the contents of an exemplarydigit list file130 corresponding to a particular set of data that includes the following phrase: “67980 minus 21345 is a lot”. As shown inFIG. 3, thedigit list file130 includes a listing of all of theunique characters131 contained within the set of data. In the particular example ofFIG. 3, there are 20unique characters131, including the “space” character. In some examples, as shown inFIG. 3, thecharacters131 within thedigit list130 may be arranged in a particular order, e.g., in ascending numerical and then alphabetical order. Thecharacters131 are shown to be on separate lines for illustrative purposes only. It will be recognized that thecharacters131 may alternatively be separated using any type of separator (e.g., whitespaces or commas) or listed without any type of separator.
• In some examples, thedigit list file130 may also list a number of additional characters not found within the set ofdata102. For example, thedigit list file130 shown inFIG. 3 may include the additional characters A, B, C, D, E, and F, collectively labeled as132.
• In certain embodiments, theadditional characters132 are sequentially listed after theunique characters131 are listed within thedigit list file130. As will be described in more detail below, theadditional characters132 may be used by thebase converter112 to convert thedata102 into a higher base of representation.
• In certain embodiments, the number of unique characters contained within a set ofdata102 is considered to be the original base of representation of that set ofdata102. For example, the data set corresponding to thedigit list130 ofFIG. 3 has an original base of representation equal to 20 because there are 20 unique characters contained therein. Eachunique character131 within thedigit list130 corresponds to a digit position within a number system having the original base of representation. For example, in the example ofFIG. 3, the character “0” corresponds to the first position with a base 20 number system, “1” corresponds to the second position with the base 20 number system, and so on through the “space” character, which corresponds to the last or twentieth position within the base 20 number system. In addition, each of theadditional characters132 corresponds to a digit position within one or more higher bases of representation to which thedata102 may be converted.
• Once thedigit list130 is created, thedigit list130 may then be used by thebase converter112 to convert the set ofdata102 into a set of data having a higher base of representation. Any known algorithm for converting from one base of representation to another may be used by thebase converter112. For example, the exemplary data set of “67980 minus 21345 is a lot” in base 20 may be converted into a set of data having any base of representation that is higher than base 20. It will be recognized that the base-converteddata102 may use one or more of theadditional characters132 within thedigit list130 to represent thedata102 at the higher base of representation.
• Once thebase converter112 converts the base of representation of the set ofdata102 into a higher base of representation, theencoder113 may encode the base-converteddata117 using any suitable fixed length encoding scheme. For example, theencoder113 may use an 8-bit ASCII encoding scheme to encode the base-converteddata117.
• The encodeddata118 may then be compressed, stored, transferred, or otherwise processed by thedata processing subsystem110. For example, the encodeddata118 may be compressed bycompression module114.
• If a user of anaccess device122 desires to access theoriginal data102, thedata processing subsystem110 may be configured to decode the encodeddata118 and convert the data back into the original base of representation. In some examples, thebase converter112 uses the information contained within thedigit list file130 to perform the base conversion.
III. Exemplary Process View
• FIG. 4 illustrates an exemplary method of encoding a set of data in a fixed length encoding scheme, according to an embodiment. WhileFIG. 4 illustrates exemplary steps according to one embodiment, other embodiments may omit, add to, reorder, and/or modify any of the steps shown inFIG. 4.
• Instep140, a set ofdata102 is analyzed to identify all of the unique characters contained therein. In some examples, thedata processing subsystem110 is configured to perform the analysis. The number of unique characters contained within the set ofdata102 is considered to be the original base of representation of the set ofdata102.
• The unique characters are then stored in a digit list, as shown instep141. The digit list may be included within a digit list file, such asdigit list file130.
• Instep142, thedata102 is converted to a higher base of representation. In certain embodiments, thebase converter112 uses the information contained within the digit list to perform the base conversion.
• The higher base of representation may be any base of representation that is higher than the original base of representation of thedata102. For example, if thedata102 is decimal data (i.e., r=10), thebase converter112 may be configured to convert the base of representation of thedata102 to any base that is greater than or equal to 11.
• However, the gains in bit utilization that are accomplished at some higher bases of representation may be offset by the extra data processing required to perform the base conversion. Hence, in certain embodiments, the higher base of representation may be chosen to optimize the bit utilization while minimizing the data processing required to perform the base conversion. For example, thedata102 may be converted into a base of representation that is the maximum power of the original base of representation permitted by the length of the particular encoding scheme. By converting thedata102 into a base of representation that is a power of the original base, the data processing required to convert thedata102 into the higher base is minimized because simple look up tables may be used to perform the base conversion.
• To illustrate, in an 8-bit encoding scheme, the maximum base size permitted by the 8 bit encoding length is 256 (because 2⁸is equal to 256). Hence, if thedata102 is decimal data (i.e., r=10), thebase converter112 may be configured to convert the base of representation of thedata102 to100 because 100 is the highest power of 10 that is less than 256. However, it will be recognized that that original base of representation of thedata102 may be converted to any higher base of representation as may serve a particular application.
• Instep143, the base-converteddata117 is encoded using any suitable fixed length encoding scheme. For example, an 8-bit ASCII encoding scheme may be used to encode the base-converteddata117. The encoded data may then be compressed, stored, transferred, or otherwise processed by thedata processing subsystem110.
• FIG. 5 illustrates an exemplary method of decoding data that has been base-converted and encoded, according to an embodiment. WhileFIG. 5 illustrates exemplary steps according to one embodiment, other embodiments may omit, add to, reorder, and/or modify any of the steps shown inFIG. 5.
• Instep150, the encodeddata118 is decoded. Anysuitable decoder120 may be configured to decode the encodeddata118.
• The base of representation of the base-converted data is then converted to the original base of representation of thedata102, as shown instep151. For example, if the base-converteddata117 is represented inbase 100 and the original base of representation of thedata102 is 10, the base-converteddata117 may be converted to base 10. In some examples, the digit list created during the encoding of thedata102 is used to convert the base-converteddata117 back into the original base of representation. The base-converteddata117 may then be encoded, as shown instep152, and transmitted to anaccess device122 so that a user may access the decodeddata102, as shown in step153.
IV. Examples
• To facilitate an understanding of the systems and methods described herein, a number of examples of optimizing bit utilization within a fixed length encoding scheme will now be given.
A. Exemplary Source Code
• Exemplary source code that may be used to perform base conversion and bit utilization calculations in connection with the following examples is given in Appendix I. The source code of Appendix I is written in ML, a modern functional language. However, it will be recognized that the code may alternatively be written in any other suitable programming language.
• The base conversion function in the source code is called B2B and accepts a numeral in string format, a first base of representation value, a second base of representation value, and a boolean value which specifies whether or not to preserve leading zeros. The base conversion function returns a numeral in string format that represents the input numeral converted to the second base of representation. A sample run of the B2B function which illustrates conversion from base 10 to base 16 with preservation of leading zeros is given below:

• 	B2B(“015”,10,16,true);
  	val it = “0F” : string

• The exemplary code also includes four bit utilization calculations called BU, rBU, rangeBU and rangeRBU. BU expects three parameters: a base of representation value, the number of bits in the fixed length encoding scheme, and one of the following strings: “best”, “worst” or “avg”. BU returns the bit utilization of a particular base of representation and encoding length pair. For example, a sample execution of the BU function for base 10 with 8-bit encoding is given below:

• 	BU(10,8,”avg”);
  	val it = 0.425 : real

• The function rBU returns the expected factor of bit utilization change associated with a conversion between a first and second base of representation. The function expects five parameters: the first base of representation, the second base of representation, the length of the encoding scheme associated with the first base of representation, the length of the encoding scheme associated with the second base of representation, and one of the following strings: “best”, “worst” or “avg”. The following sample rBU execution shows the average case bit utilization change when data is converted from base 10 to base 26, each with 8-bit encoding:

• 	rBU(10,26,8,8,”avg”);
  	val it = 0.712903225806 : real

• The function rangeBU accepts a base value and the number of bits of an encoding scheme and returns best, average, and worst case bit utilization values. The following rangeBU execution shows the best, average, and worst case bit utilization values for the bases10 and26, each with 8-bit encoding:

• 	rangeBU(10,8);
  	val it = (0.5,0.425,0.375) : real*real*real
  	rangeBU(26,8);
  	val it = (0.625,0.596153846154,0.5) : real*real*real

• Similarly, the function rangeRBU accepts a first base of representation, a second base of representation, a length of the encoding scheme associated with the first base of representation, and a length of the encoding scheme associated with the second base of representation. The function rangeRBU returns best, average, and worst case relative bit utilization values between the first and second bases of representation. The following rangeRBU execution shows the relative best, average, and worst case bit utilization values between base 10 and base 26:

• 	rangeRBU(10,26,8,8);
  	val it = (0.6,0.712903225806,1.0) : real*real*real

B. First Example
• In a first example, a data file comprising 32,634,193 decimal telephone numbers was encoded using an 8-bit encoding scheme. Each telephone number included 10 characters or digits. Each telephone number occupied its own line within the data file.
• The data file was first analyzed by thedata processing subsystem110. Because the data file included only telephone numbers, 10 unique characters (the numerals 0-9) were found by thedata processing system110. Hence, the data was considered to be base 10 data. For comparative purposes, the newline characters within the data file were ignored.
• A digit list file named “AlphaBet.sml” was then created, the contents of which are shown in Appendix II. As shown in Appendix II, the first ten digits listed correspond to the ten unique characters found within the data file. A number of additional digits are also included within the digit list file. These additional digits include a number of ASCII symbols and were used to convert the data file to a higher base of representation.
• A number of trials were then run wherein the base of representation of the data file was converted to each of a number of different bases of representation ranging from base 2 to base 245. Each time, the base-converted data was encoded using 8-bit encoding. The size of the resultant data file was then measured by calculating the full file size and subtracting one byte per line for the newline characters. Table 3 shows a select number of resultant data file sizes:

• 	TABLE 3
  	Base of Data File	Size in Megabytes

  	10	311.22
  	62	186.81
  	93	167.39
  	100	155.61

• As shown in Table 3, data having the initial base 10 data consumed 311.22 megabytes of disk space. However, after the data file had been converted to base 62 and encoded, the resultant data file only consumed 186.81 megabytes. Likewise, the data in base 93 consumed 167.39 megabytes and the data inbase 100 consumed 155.61 megabytes. The complete results of the trials are shown in Appendix III.
• Hence, as shown in Appendix III, conversion of base 10 data to a higher base of representation resulted in substantial bit utilization optimization. For example, by converting the base 10 data to base 100 data, the resultant data file was approximately half the size as the original data file.
C. Second Example
• In another example, a data file comprising the entire text from the King James version of the Bible was encoded using an 8-bit encoding scheme. The data within the file was first analyzed by thedata processing subsystem110 and found to contain 87 unique characters. Hence, the data was considered to be base eighty-seven data.
• A digit list file named “bible_alphabet.sml” was then created, the contents of which are shown in Appendix IV. The first 87 characters listed within the digit list file correspond to the 87 unique characters found within the data file. A number of additional digits are also included within the digit list file. These additional digits include a number of ASCII symbols and were used to convert the data file to a higher base of representation.
• A number of trials were then run wherein the base of representation of the data file was converted to each of a number of different bases of representation ranging from base 2 to base 247. Each time, the base-converted data was encoded using 8-bit encoding. The size of the resultant data file was then calculated. Table 4 shows a select number of resultant data file sizes:

• 	TABLE 4
  	Base of Data File	Size in Megabytes

  	87	3.49
  	150	3.40
  	200	3.28
  	247	3.16

• As shown in Table 4, data having the initial base eighty-seven consumed 3.49 megabytes of disk space. However, after the data file had been converted tobase 150 and encoded, the resultant data file consumed 3.40 megabytes. Likewise, the data in base 200 consumed 3.28 megabytes and the data in base 247 consumed 3.16 megabytes. The complete results of the trials are shown in Appendix V.
V. Alternative Embodiments
• The preceding description has been presented only to illustrate and describe embodiments of the invention. It is not intended to be exhaustive or to limit the invention to any precise form disclosed. The invention may be practiced otherwise than is specifically explained and illustrated without departing from its spirit or scope. It is intended that the scope of the invention be defined by the following claims.

• APPENDIX II
  (*

  *	File name - AlphaBet.sml
  *	The digits in this Alphabet are chosen to match RFC 1924

  *	(http://www.faqs.org/rfcs/rfc1924.html)

  *	for bases from 2 through 85.

  *)

  val AlphaBet=

  (

  “0123456789”{circumflex over ( )}

  (* 0 −> 9 *) (*ASCII: 48-57*)

  (*

  1

  2

  3

  *	01234567890123456789012345 *)
  	“ABCDEFGHIJKLMNOPQRSTUVWXYZ”{circumflex over ( )} (*ASCII: 65-90*)

  (*

  3

  4

  5

  6

  *	67890123456789012345678901 *)
  	“abcdefghijklmnopqrstuvwxyz”{circumflex over ( )} (*ASCII: 97-122*)

  	“!” {circumflex over ( )}	(*62 / ASC 33 *)
  	“#” {circumflex over ( )}	(*63 / ASC 35 *)
  	“$” {circumflex over ( )}	(*64 / ASC 36 *)
  	“%” {circumflex over ( )}	(*65 / ASC 37 *)
  	“&” {circumflex over ( )}	(*66 / ASC 38 *)
  	“(” {circumflex over ( )}	(*67 / ASC 40 *)
  	“)” {circumflex over ( )}	(*68 / ASC 41 *)
  	“*” {circumflex over ( )}	(*69 / ASC 42 *)
  	“+” {circumflex over ( )}	(*70 / ASC 43 *)
  	“−” {circumflex over ( )}	(*71 / ASC 44 *)
  	“;” {circumflex over ( )}	(*72 / ASC 45 *)
  	“<” {circumflex over ( )}	(*73 / ASC 60 *)
  	“=” {circumflex over ( )}	(*74 / ASC 61 *)
  	“>” {circumflex over ( )}	(*75 / ASC 62 *)
  	“?” {circumflex over ( )}	(*76 / ASC 63 *)
  	“@” {circumflex over ( )}	(*77 / ASC 64 *)
  	“{circumflex over ( )}” {circumflex over ( )}	(*78 / ASC 94 *)
  	“_” {circumflex over ( )}	(*79 / ASC 95 *)
  	“{grave over ( )}” {circumflex over ( )}	(*80 / ASC 96 *)
  	“{” {circumflex over ( )}	(*81 / ASC 123 *)
  	“|” {circumflex over ( )}	(*82 / ASC 124 *)
  	“}” {circumflex over ( )}	(*83 / ASC 125 *)
  	“~” {circumflex over ( )}	(*84 / ASC 126 *)
  	“:” {circumflex over ( )}	(*85 / ASC 58 *)
  	“,” {circumflex over ( )}	(*86 / ASC 44 *)
  	“.” {circumflex over ( )}	(*87 / ASC 46 *)
  	“/” {circumflex over ( )}	(*88 / ASC 47 *)
  	“[” {circumflex over ( )}	(*89 / ASC 91 *)
  	“]” {circumflex over ( )}	(*90 / ASC 93 *)
  	“\” {circumflex over ( )}	(*91 / ASC 34 *)
  	“′” {circumflex over ( )}	(*92 / ASC 39 *)
  	“\\” {circumflex over ( )}	(*93 / ASC 92 *)

  (*	For number systems using the digits,
  *	from here on, I/O becomes more complicated

  *)
  (*	Extended ASCII & “ ” *)
  	“\128” {circumflex over ( )}	(*94*)
  	“\129” {circumflex over ( )}	(*95*)
  	“\130” {circumflex over ( )}	(*96*)
  	“\131” {circumflex over ( )}	(*97*)
  	“\132” {circumflex over ( )}	(*98*)
  	“\133” {circumflex over ( )}	(*99*)
  	“\134” {circumflex over ( )}	(*100*)
  	“\135” {circumflex over ( )}	(*101*)
  	“\136” {circumflex over ( )}	(*102*)
  	“\137” {circumflex over ( )}	(*103*)
  	“\138” {circumflex over ( )}	(*104*)
  	“\139” {circumflex over ( )}	(*105*)
  	“\140” {circumflex over ( )}	(*106*)
  	“\141” {circumflex over ( )}	(*107*)
  	“\142” {circumflex over ( )}	(*108*)
  	“\143” {circumflex over ( )}	(*109*)
  	“\144” {circumflex over ( )}	(*110*)
  	“\145” {circumflex over ( )}	(*111*)
  	“\146” {circumflex over ( )}	(*112*)
  	“\147” {circumflex over ( )}	(*113*)
  	“\148” {circumflex over ( )}	(*114*)
  	“\149” {circumflex over ( )}	(*115*)
  	“\150” {circumflex over ( )}	(*116*)
  	“\151” {circumflex over ( )}	(*117*)
  	“\152” {circumflex over ( )}	(*118*)
  	“\153” {circumflex over ( )}	(*119*)
  	“\154” {circumflex over ( )}	(*120*)
  	“\155” {circumflex over ( )}	(*121*)
  	“\156” {circumflex over ( )}	(*122*)
  	“\157” {circumflex over ( )}	(*123*)
  	“\158” {circumflex over ( )}	(*124*)
  	“\159” {circumflex over ( )}	(*125*)
  	“\160” {circumflex over ( )}	(*126*)
  	“\161” {circumflex over ( )}	(*127*)
  	“\162” {circumflex over ( )}	(*128*)
  	“\163” {circumflex over ( )}	(*129*)
  	“\164” {circumflex over ( )}	(*130*)
  	“\165” {circumflex over ( )}	(*131*)
  	“\166” {circumflex over ( )}	(*132*)
  	“\167” {circumflex over ( )}	(*133*)
  	“\168” {circumflex over ( )}	(*134*)
  	“\169” {circumflex over ( )}	(*135*)
  	“\170” {circumflex over ( )}	(*136*)
  	“\171” {circumflex over ( )}	(*137*)
  	“\172” {circumflex over ( )}	(*138*)
  	“\173” {circumflex over ( )}	(*139*)
  	“\174” {circumflex over ( )}	(*140*)
  	“\175” {circumflex over ( )}	(*141*)
  	“\176” {circumflex over ( )}	(*142*)
  	“\177” {circumflex over ( )}	(*143*)
  	“\178” {circumflex over ( )}	(*144*)
  	“\179” {circumflex over ( )}	(*145*)
  	“\180” {circumflex over ( )}	(*146*)
  	“\181” {circumflex over ( )}	(*147*)
  	“\182” {circumflex over ( )}	(*148*)
  	“\183” {circumflex over ( )}	(*149*)
  	“\184” {circumflex over ( )}	(*150*)
  	“\185” {circumflex over ( )}	(*151*)
  	“\186” {circumflex over ( )}	(*152*)
  	“\187” {circumflex over ( )}	(*153*)
  	“\188” {circumflex over ( )}	(*154*)
  	“\189” {circumflex over ( )}	(*155*)
  	“\190” {circumflex over ( )}	(*156*)
  	“\191” {circumflex over ( )}	(*157*)
  	“\192” {circumflex over ( )}	(*158*)
  	“\193” {circumflex over ( )}	(*159*)
  	“\194” {circumflex over ( )}	(*160*)
  	“\195” {circumflex over ( )}	(*161*)
  	“\196” {circumflex over ( )}	(*162*)
  	“\197” {circumflex over ( )}	(*163*)
  	“\198” {circumflex over ( )}	(*164*)
  	“\199” {circumflex over ( )}	(*165*)
  	“\200” {circumflex over ( )}	(*166*)
  	“\201” {circumflex over ( )}	(*167*)
  	“\202” {circumflex over ( )}	(*168*)
  	“\203” {circumflex over ( )}	(*169*)
  	“\204” {circumflex over ( )}	(*170*)
  	“\205” {circumflex over ( )}	(*171*)
  	“\206” {circumflex over ( )}	(*172*)
  	“\207” {circumflex over ( )}	(*173*)
  	“\208” {circumflex over ( )}	(*174*)
  	“\209” {circumflex over ( )}	(*175*)
  	“\210” {circumflex over ( )}	(*176*)
  	“\211” {circumflex over ( )}	(*177*)
  	“\212” {circumflex over ( )}	(*178*)
  	“\213” {circumflex over ( )}	(*179*)
  	“\214” {circumflex over ( )}	(*180*)
  	“\215” {circumflex over ( )}	(*181*)
  	“\216” {circumflex over ( )}	(*182*)
  	“\217” {circumflex over ( )}	(*183*)
  	“\218” {circumflex over ( )}	(*184*)
  	“\219” {circumflex over ( )}	(*185*)
  	“\220” {circumflex over ( )}	(*186*)
  	“\221” {circumflex over ( )}	(*187*)
  	“\222” {circumflex over ( )}	(*188*)
  	“\223” {circumflex over ( )}	(*189*)
  	“\224” {circumflex over ( )}	(*190*)
  	“\225” {circumflex over ( )}	(*191*)
  	“\226” {circumflex over ( )}	(*192*)
  	“\227” {circumflex over ( )}	(*193*)
  	“\228” {circumflex over ( )}	(*194*)
  	“\229” {circumflex over ( )}	(*195*)
  	“\230” {circumflex over ( )}	(*196*)
  	“\231” {circumflex over ( )}	(*197*)
  	“\232” {circumflex over ( )}	(*198*)
  	“\233” {circumflex over ( )}	(*199*)
  	“\234” {circumflex over ( )}	(*200*)
  	“\235” {circumflex over ( )}	(*201*)
  	“\236” {circumflex over ( )}	(*202*)
  	“\237” {circumflex over ( )}	(*203*)
  	“\238” {circumflex over ( )}	(*204*)
  	“\239” {circumflex over ( )}	(*205*)
  	“\240” {circumflex over ( )}	(*206*)
  	“\241” {circumflex over ( )}	(*207*)
  	“\242” {circumflex over ( )}	(*208*)
  	“\243” {circumflex over ( )}	(*209*)
  	“\244” {circumflex over ( )}	(*210*)
  	“\245” {circumflex over ( )}	(*211*)
  	“\246” {circumflex over ( )}	(*212*)
  	“\247” {circumflex over ( )}	(*213*)
  	“\248” {circumflex over ( )}	(*214*)
  	“\249” {circumflex over ( )}	(*215*)
  	“\250” {circumflex over ( )}	(*216*)
  	“\251” {circumflex over ( )}	(*217*)
  	“\252” {circumflex over ( )}	(*218*)
  	“\253” {circumflex over ( )}	(*219*)
  	“\254” {circumflex over ( )}	(*220*)
  	“\255” {circumflex over ( )}	(*247*)

  (*	Other non-printable characers from basic ASCII *)

  	“\001” {circumflex over ( )}	(*221*)
  	“\002” {circumflex over ( )}	(*222*)
  	“\003” {circumflex over ( )}	(*223*)
  	“\004” {circumflex over ( )}	(*224*)
  	“\005” {circumflex over ( )}	(*225*)
  	“\006” {circumflex over ( )}	(*226*)
  	“\007” {circumflex over ( )}	(*227*)
  	“\008” {circumflex over ( )}	(*228*)
  	“\014” {circumflex over ( )}	(*229*)
  	“\015” {circumflex over ( )}	(*230*)
  	“\016” {circumflex over ( )}	(*231*)
  	“\017” {circumflex over ( )}	(*232*)
  	“\018” {circumflex over ( )}	(*233*)
  	“\019” {circumflex over ( )}	(*234*)
  	“\020” {circumflex over ( )}	(*235*)
  	“\021” {circumflex over ( )}	(*236*)
  	“\022” {circumflex over ( )}	(*237*)
  	“\023” {circumflex over ( )}	(*238*)
  	“\024” {circumflex over ( )}	(*239*)
  	“\025” {circumflex over ( )}	(*240*)
  	“\026” {circumflex over ( )}	(*241*)
  	“\027” {circumflex over ( )}	(*242*)
  	“\028” {circumflex over ( )}	(*243*)
  	“\029” {circumflex over ( )}	(*244*)
  	“\030” {circumflex over ( )}	(*245*)
  	“\031” {circumflex over ( )}	(*246*)

  “ ”

  (* [SPACE / ASC 32] *)

  (*248*)

  “\127” {circumflex over ( )}

  (*249*)

  	“\012” {circumflex over ( )}	[FF]	(*250*)
  	“\009” {circumflex over ( )}	[TAB]	(*251*)
  	“\010” {circumflex over ( )}	[NL]	(*252*)

  “\011” {circumflex over ( )}

  (*253*)

  “\013” {circumflex over ( )}

  [CR]

  (*254*)

  	“\000”	(*255*)
  *)
  );

• 	APPENDIX III
  	Base of Data File	Size in Bytes

  	2	1,063,468,262
  	3	676,684,671
  	4	542,086,267
  	5	471,473,922
  	7	391,680,665
  	8	361,712,665
  	10	326,341,930
  	12	312,465,742
  	13	293,707,737
  	15	288,840,417
  	17	273,412,321
  	18	261,073,544
  	20	261,073,544
  	22	256,281,086
  	25	243,034,571
  	27	228,547,612
  	28	228,439,351
  	30	228,439,351
  	32	228,517,830
  	33	228,439,351
  	35	228,439,351
  	37	223,651,499
  	38	223,516,739
  	40	219,356,029
  	42	212,920,664
  	43	208,092,043
  	45	199,722,825
  	47	195,915,711
  	48	195,805,158
  	50	195,805,158
  	52	195,907,040
  	53	195,805,158
  	55	195,805,158
  	57	195,898,013
  	58	195,805,158
  	60	195,805,158
  	62	195,889,598
  	63	195,805,158
  	64	195,805,158
  	65	195,805,158
  	67	195,885,241
  	68	195,805,158
  	70	195,805,158
  	72	195,879,055
  	73	194,367,268
  	75	190,958,776
  	77	191,011,592
  	78	190,882,546
  	80	187,124,505
  	82	187,204,256
  	83	187,123,305
  	85	182,917,078
  	87	182,990,144
  	88	180,645,181
  	90	179,624,926
  	93	175,425,614
  	94	169,366,577
  	95	168,763,050
  	98	165,907,507
  	99	164,983,777
  	100	163,170,965
  	103	163,170,965
  	104	163,277,825
  	105	163,170,965
  	108	163,170,965
  	109	163,276,820
  	110	163,170,965
  	113	163,170,965
  	114	163,275,757
  	115	163,170,965
  	116	163,170,965
  	118	163,170,965
  	119	163,274,570
  	120	163,170,965
  	123	163,170,965
  	124	163,273,276
  	125	163,170,965
  	128	163,170,965
  	129	163,272,125
  	130	163,170,965
  	133	163,170,965
  	134	163,270,251
  	135	163,170,965
  	138	163,170,965
  	139	163,269,226
  	140	163,170,965
  	143	163,170,965
  	144	163,267,162
  	145	163,170,965
  	148	163,170,965
  	149	163,264,829
  	150	163,170,965
  	153	163,170,965
  	154	163,263,470
  	155	163,170,965
  	158	163,170,965
  	159	163,261,247
  	160	163,170,965
  	163	163,170,965
  	164	163,258,526
  	165	163,170,965
  	168	163,170,965
  	169	163,256,339
  	170	163,170,965
  	173	163,170,965
  	174	163,254,144
  	175	163,170,965
  	178	163,170,965
  	179	163,252,143
  	180	163,170,965
  	183	163,170,965
  	184	163,250,426
  	185	163,170,965
  	188	163,170,965
  	189	163,249,290
  	190	163,170,965
  	193	161,170,965
  	194	163,247,248
  	195	163,170,965
  	198	161,170,965
  	199	163,245,596
  	200	163,170,965
  	203	161,170,965
  	204	163,242,992
  	205	163,170,965
  	208	161,170,965
  	209	163,241,649
  	210	163,170,965
  	213	161,782,440
  	214	161,288,708
  	215	159,714,359
  	218	158,324,583
  	219	158,403,524
  	220	158,324,583
  	223	158,303,645
  	224	158,382,425
  	225	158,303,645
  	228	158,298,845
  	229	158,376,821
  	230	158,248,353
  	233	158,248,353
  	234	158,325,926
  	235	154,985,244
  	238	154,490,312
  	239	154,575,628
  	240	154,490,312
  	243	154,489,112
  	244	154,574,011
  	245	154,489,112

• APPENDIX IV
  (*

  *	File name - bibl_alphabet.sml
  *	Custom alphabet for the bible.

  *)

  val AlphaBet=

  (

  “0123456789”{circumflex over ( )}

  (* 0 −> 9 *) (*ASCII: 48-57*)

  (*

  1

  2

  3

  *	01234567890123456789012345 *)
  	“ABCDEFGHIJKLMNOPQRSTUVWXYZ”{circumflex over ( )} (*ASCII: 65-90*)

  (*

  3

  4

  5

  6

  *	67890123456789012345678901 *)
  	“abcdefghijklmnopqrstuvwxyz”{circumflex over ( )} (*ASCII: 97-122*)

  	“$” {circumflex over ( )}	(*62*)
  	“#” {circumflex over ( )}	(*63*)
  	“%” {circumflex over ( )}	(*64*)
  	“@” {circumflex over ( )}	(*65*)
  	“/” {circumflex over ( )}	(*66*)
  	“[” {circumflex over ( )}	(*67*)
  	“\” {circumflex over ( )}	(*68*)
  	“−” {circumflex over ( )}	(*69*)
  	“*” {circumflex over ( )}	(*70*)
  	“(” {circumflex over ( )}	(*71*)
  	“!” {circumflex over ( )}	(*72*)
  	“′” {circumflex over ( )}	(*73*)
  	“?” {circumflex over ( )}	(*74*)
  	“;” {circumflex over ( )}	(*75*)
  	“.” {circumflex over ( )}	(*76*)
  	“:” {circumflex over ( )}	(*77*)
  	“,” {circumflex over ( )}	(*78*)
  	“~” {circumflex over ( )}	(*79*)
  	“)” {circumflex over ( )}	(*80*)
  	“]” {circumflex over ( )}	(*81*)
  	“+” {circumflex over ( )}	(*82*)
  	“=” {circumflex over ( )}	(*83*)
  	“<” {circumflex over ( )}	(*84*)
  	“>” {circumflex over ( )}	(*85*)
  	“_” {circumflex over ( )}	(*86*)
  	“&” {circumflex over ( )}	(*87*)
  	“{circumflex over ( )}” {circumflex over ( )}	(*88*)
  	“{grave over ( )}” {circumflex over ( )}	(*89*)
  	“{” {circumflex over ( )}	(*90*)
  	“|” {circumflex over ( )}	(*91*)
  	“}” {circumflex over ( )}	(*92*)
  	“\\” {circumflex over ( )}	(*93*)
  (*	Extended ASCII & “ ” *)

  	“\128” {circumflex over ( )}	(*94*)
  	“\129” {circumflex over ( )}	(*95*)
  	“\130” {circumflex over ( )}	(*96*)
  	“\131” {circumflex over ( )}	(*97*)
  	“\132” {circumflex over ( )}	(*98*)
  	“\133” {circumflex over ( )}	(*99*)
  	“\134” {circumflex over ( )}	(*100*)
  	“\135” {circumflex over ( )}	(*101*)
  	“\136” {circumflex over ( )}	(*102*)
  	“\137” {circumflex over ( )}	(*103*)
  	“\138” {circumflex over ( )}	(*104*)
  	“\139” {circumflex over ( )}	(*105*)
  	“\140” {circumflex over ( )}	(*106*)
  	“\141” {circumflex over ( )}	(*107*)
  	“\142” {circumflex over ( )}	(*108*)
  	“\143” {circumflex over ( )}	(*109*)
  	“\144” {circumflex over ( )}	(*110*)
  	“\145” {circumflex over ( )}	(*111*)
  	“\146” {circumflex over ( )}	(*112*)
  	“\147” {circumflex over ( )}	(*113*)
  	“\148” {circumflex over ( )}	(*114*)
  	“\149” {circumflex over ( )}	(*115*)
  	“\150” {circumflex over ( )}	(*116*)
  	“\151” {circumflex over ( )}	(*117*)
  	“\152” {circumflex over ( )}	(*118*)
  	“\153” {circumflex over ( )}	(*119*)
  	“\154” {circumflex over ( )}	(*120*)
  	“\155” {circumflex over ( )}	(*121*)
  	“\156” {circumflex over ( )}	(*122*)
  	“\157” {circumflex over ( )}	(*123*)
  	“\158” {circumflex over ( )}	(*124*)
  	“\159” {circumflex over ( )}	(*125*)
  	“\160” {circumflex over ( )}	(*126*)
  	“\161” {circumflex over ( )}	(*127*)
  	“\162” {circumflex over ( )}	(*128*)
  	“\163” {circumflex over ( )}	(*129*)
  	“\164” {circumflex over ( )}	(*130*)
  	“\165” {circumflex over ( )}	(*131*)
  	“\166” {circumflex over ( )}	(*132*)
  	“\167” {circumflex over ( )}	(*133*)
  	“\168” {circumflex over ( )}	(*134*)
  	“\169” {circumflex over ( )}	(*135*)
  	“\170” {circumflex over ( )}	(*136*)
  	“\171” {circumflex over ( )}	(*137*)
  	“\172” {circumflex over ( )}	(*138*)
  	“\173” {circumflex over ( )}	(*139*)
  	“\174” {circumflex over ( )}	(*140*)
  	“\175” {circumflex over ( )}	(*141*)
  	“\176” {circumflex over ( )}	(*142*)
  	“\177” {circumflex over ( )}	(*143*)
  	“\178” {circumflex over ( )}	(*144*)
  	“\179” {circumflex over ( )}	(*145*)
  	“\180” {circumflex over ( )}	(*146*)
  	“\181” {circumflex over ( )}	(*147*)
  	“\182” {circumflex over ( )}	(*148*)
  	“\183” {circumflex over ( )}	(*149*)
  	“\184” {circumflex over ( )}	(*150*)
  	“\185” {circumflex over ( )}	(*151*)
  	“\186” {circumflex over ( )}	(*152*)
  	“\187” {circumflex over ( )}	(*153*)
  	“\188” {circumflex over ( )}	(*154*)
  	“\189” {circumflex over ( )}	(*155*)
  	“\190” {circumflex over ( )}	(*156*)
  	“\191” {circumflex over ( )}	(*157*)
  	“\192” {circumflex over ( )}	(*158*)
  	“\193” {circumflex over ( )}	(*159*)
  	“\194” {circumflex over ( )}	(*160*)
  	“\195” {circumflex over ( )}	(*161*)
  	“\196” {circumflex over ( )}	(*162*)
  	“\197” {circumflex over ( )}	(*163*)
  	“\198” {circumflex over ( )}	(*164*)
  	“\199” {circumflex over ( )}	(*165*)
  	“\200” {circumflex over ( )}	(*166*)
  	“\201” {circumflex over ( )}	(*167*)
  	“\202” {circumflex over ( )}	(*168*)
  	“\203” {circumflex over ( )}	(*169*)
  	“\204” {circumflex over ( )}	(*170*)
  	“\205” {circumflex over ( )}	(*171*)
  	“\206” {circumflex over ( )}	(*172*)
  	“\207” {circumflex over ( )}	(*173*)
  	“\208” {circumflex over ( )}	(*174*)
  	“\209” {circumflex over ( )}	(*175*)
  	“\210” {circumflex over ( )}	(*176*)
  	“\211” {circumflex over ( )}	(*177*)
  	“\212” {circumflex over ( )}	(*178*)
  	“\213” {circumflex over ( )}	(*179*)
  	“\214” {circumflex over ( )}	(*180*)
  	“\215” {circumflex over ( )}	(*181*)
  	“\216” {circumflex over ( )}	(*182*)
  	“\217” {circumflex over ( )}	(*183*)
  	“\218” {circumflex over ( )}	(*184*)
  	“\219” {circumflex over ( )}	(*185*)
  	“\220” {circumflex over ( )}	(*186*)
  	“\221” {circumflex over ( )}	(*187*)
  	“\222” {circumflex over ( )}	(*188*)
  	“\223” {circumflex over ( )}	(*189*)
  	“\224” {circumflex over ( )}	(*190*)
  	“\225” {circumflex over ( )}	(*191*)
  	“\226” {circumflex over ( )}	(*192*)
  	“\227” {circumflex over ( )}	(*193*)
  	“\228” {circumflex over ( )}	(*194*)
  	“\229” {circumflex over ( )}	(*195*)
  	“\230” {circumflex over ( )}	(*196*)
  	“\231” {circumflex over ( )}	(*197*)
  	“\232” {circumflex over ( )}	(*198*)
  	“\233” {circumflex over ( )}	(*199*)
  	“\234” {circumflex over ( )}	(*200*)
  	“\235” {circumflex over ( )}	(*201*)
  	“\236” {circumflex over ( )}	(*202*)
  	“\237” {circumflex over ( )}	(*203*)
  	“\238” {circumflex over ( )}	(*204*)
  	“\239” {circumflex over ( )}	(*205*)
  	“\240” {circumflex over ( )}	(*206*)
  	“\241” {circumflex over ( )}	(*207*)
  	“\242” {circumflex over ( )}	(*208*)
  	“\243” {circumflex over ( )}	(*209*)
  	“\244” {circumflex over ( )}	(*210*)
  	“\245” {circumflex over ( )}	(*211*)
  	“\246” {circumflex over ( )}	(*212*)
  	“\247” {circumflex over ( )}	(*213*)
  	“\248” {circumflex over ( )}	(*214*)
  	“\249” {circumflex over ( )}	(*215*)
  	“\250” {circumflex over ( )}	(*216*)
  	“\251” {circumflex over ( )}	(*217*)
  	“\252” {circumflex over ( )}	(*218*)
  	“\253” {circumflex over ( )}	(*219*)
  	“\254” {circumflex over ( )}	(*220*)
  	“\255” {circumflex over ( )}	(*221*)

  (*	Other non-printable characers from basic ASCII *)

  	“\001” {circumflex over ( )}	(*222*)
  	“\002” {circumflex over ( )}	(*223*)
  	“\003” {circumflex over ( )}	(*224*)
  	“\004” {circumflex over ( )}	(*225*)
  	“\005” {circumflex over ( )}	(*226*)
  	“\006” {circumflex over ( )}	(*227*)
  	“\007” {circumflex over ( )}	(*228*)
  	“\008” {circumflex over ( )}	(*229*)
  	“\014” {circumflex over ( )}	(*230*)
  	“\015” {circumflex over ( )}	(*231*)
  	“\016” {circumflex over ( )}	(*232*)
  	“\017” {circumflex over ( )}	(*233*)
  	“\018” {circumflex over ( )}	(*234*)
  	“\019” {circumflex over ( )}	(*235*)
  	“\020” {circumflex over ( )}	(*236*)
  	“\021” {circumflex over ( )}	(*237*)
  	“\022” {circumflex over ( )}	(*238*)
  	“\023” {circumflex over ( )}	(*239*)
  	“\024” {circumflex over ( )}	(*240*)
  	“\025” {circumflex over ( )}	(*241*)
  	“\026” {circumflex over ( )}	(*242*)
  	“\027” {circumflex over ( )}	(*243*)
  	“\028” {circumflex over ( )}	(*244*)
  	“\029” {circumflex over ( )}	(*245*)
  	“\030” {circumflex over ( )}	(*246*)
  	“\031” {circumflex over ( )}	(*247*)

  “ ”

  (*[SPACE / ASC 32] *)

  (*248*)

  “\127” {circumflex over ( )}

  (*249*)

  “\012” {circumflex over ( )}

  [FF]

  (*250*)

  “\009” {circumflex over ( )}

  [TAB]

  (*251*)

  “\010” {circumflex over ( )}

  [NL]

  (*252*)

  “\011” {circumflex over ( )}

  (*253*)

  “\013” {circumflex over ( )}

  [CR]

  (*254*)

  “\000”

  (*255*)

  *)

  );

• 	APPENDIX V
  	Base of Data File	Size in Megabytes

  	2	21,982,207
  	3	13,891,885
  	4	11,226,719
  	5	9,700,112
  	6	8,752,700
  	7	8,058,622
  	8	7,674,147
  	9	7,009,352
  	10	6,902,673
  	11	6,704,089
  	12	6,500,949
  	13	6,245,138
  	14	6,052,972
  	15	5,950,329
  	16	5,804,322
  	17	5,671,090
  	18	5,569,445
  	19	5,400,268
  	20	5,375,653
  	21	5,345,009
  	22	5,269,662
  	23	5,141,684
  	24	5,087,990
  	25	5,038,414
  	26	4,928,603
  	27	4,882,851
  	28	4,863,598
  	29	4,853,961
  	30	4,820,869
  	31	4,761,423
  	32	4,729,808
  	33	4,632,875
  	34	4,611,284
  	35	4,601,535
  	36	4,579,583
  	37	4,537,091
  	38	4,516,511
  	39	4,458,061
  	40	4,448,721
  	41	4,433,879
  	42	4,413,744
  	43	4,395,477
  	44	4,368,141
  	45	4,351,424
  	46	4,341,766
  	47	4,324,287
  	48	4,314,876
  	49	4,303,444
  	50	4,292,579
  	51	4,280,549
  	52	4,271,864
  	53	4,267,454
  	54	4,259,534
  	55	4,256,432
  	56	4,251,285
  	57	4,240,193
  	58	4,225,703
  	59	4,222,702
  	60	4,220,041
  	61	4,215,819
  	62	4,200,104
  	63	4,173,527
  	64	4,172,134
  	65	4,166,924
  	66	4,104,159
  	67	4,057,680
  	68	4,052,626
  	69	4,041,945
  	70	4,006,507
  	71	3,991,208
  	72	3,972,151
  	73	3,942,034
  	74	3,910,111
  	75	3,819,009
  	76	3,783,581
  	77	3,765,267
  	78	3,695,438
  	79	3,638,504
  	80	3,579,452
  	81	3,541,959
  	82	3,518,685
  	83	3,501,749
  	84	3,495,685
  	85	3,494,789
  	86	3,494,773
  	87	3,494,772
  	88	3,490,454
  	89	3,487,582
  	90	3,485,921
  	91	3,485,705
  	92	3,485,705
  	93	3,485,705
  	94	3,485,705
  	95	3,485,705
  	96	3,485,704
  	97	3,485,704
  	98	3,485,703
  	99	3,485,703
  	100	3,485,703
  	101	3,485,702
  	102	3,485,692
  	103	3,485,691
  	104	3,484,247
  	105	3,481,838
  	106	3,481,824
  	107	3,481,800
  	108	3,480,767
  	109	3,480,713
  	110	3,480,428
  	111	3,479,332
  	112	3,478,668
  	113	3,478,507
  	114	3,478,317
  	115	3,477,184
  	116	3,475,883
  	117	3,475,257
  	118	3,474,418
  	119	3,473,612
  	120	3,472,811
  	121	3,471,605
  	122	3,469,583
  	123	3,468,924
  	124	3,466,391
  	125	3,465,466
  	126	3,463,824
  	127	3,461,979
  	128	3,460,997
  	129	3,459,768
  	130	3,458,034
  	131	3,453,468
  	132	3,452,684
  	133	3,450,549
  	134	3,449,688
  	135	3,448,004
  	136	3,444,703
  	137	3,440,259
  	138	3,436,738
  	139	3,434,783
  	140	3,432,823
  	141	3,431,438
  	142	3,428,513
  	143	3,425,904
  	144	3,421,723
  	145	3,420,240
  	146	3,418,321
  	147	3,413,093
  	148	3,409,361
  	149	3,406,410
  	150	3,404,596
  	151	3,403,823
  	152	3,401,863
  	153	3,397,989
  	154	3,396,388
  	155	3,391,073
  	156	3,390,161
  	157	3,388,072
  	158	3,385,582
  	159	3,382,717
  	160	3,375,068
  	161	3,373,314
  	162	3,370,872
  	163	3,369,577
  	164	3,366,600
  	165	3,365,814
  	166	3,364,076
  	167	3,360,560
  	168	3,356,210
  	169	3,354,433
  	170	3,346,191
  	171	3,344,470
  	172	3,341,132
  	173	3,340,962
  	174	3,339,960
  	175	3,339,777
  	176	3,339,380
  	177	3,339,108
  	178	3,338,678
  	179	3,336,579
  	180	3,331,790
  	181	3,327,685
  	182	3,325,642
  	183	3,322,887
  	184	3,319,271
  	185	3,316,138
  	186	3,314,193
  	187	3,310,523
  	188	3,309,068
  	189	3,307,166
  	190	3,303,632
  	191	3,302,836
  	192	3,298,834
  	193	3,296,735
  	194	3,290,655
  	195	3,286,044
  	196	3,284,584
  	197	3,281,515
  	198	3,280,980
  	199	3,280,661
  	200	3,280,577
  	201	3,280,161
  	202	3,279,481
  	203	3,278,524
  	204	3,278,215
  	205	3,277,808
  	206	3,277,808
  	207	3,277,597
  	208	3,277,141
  	209	3,276,973
  	210	3,276,969
  	211	3,276,950
  	212	3,276,475
  	213	3,275,877
  	214	3,271,238
  	215	3,269,640
  	216	3,265,297
  	217	3,261,873
  	218	3,260,599
  	219	3,257,985
  	220	3,254,741
  	221	3,249,502
  	222	3,247,099
  	223	3,243,411
  	224	3,237,946
  	225	3,237,216
  	226	3,236,804
  	227	3,236,445
  	228	3,235,277
  	229	3,232,257
  	230	3,229,623
  	231	3,228,115
  	232	3,227,686
  	233	3,226,145
  	234	3,224,405
  	235	3,223,852
  	236	3,222,053
  	237	3,201,174
  	238	3,184,039
  	239	3,182,563
  	240	3,181,547
  	241	3,170,751
  	242	3,166,394
  	243	3,164,403
  	244	3,164,098
  	245	3,163,546
  	246	3,162,987
  	247	3,162,709

Claims (21)

1. A system comprising:

a data source configured to provide a set of data; and

a data processing subsystem communicatively coupled to said data source and configured to

identify a total number of unique characters within said set of data, said set of data having an original base of representation equal to said total number of unique characters;

convert said set of data to a higher base of representation, said higher base of representation being greater in value than said original base of representation; and

encode said base-converted data with a fixed-length encoding scheme.

2. The system ofclaim 1, wherein said data processing subsystem is further configured to store said unique characters within a digit list file.

3. The system ofclaim 2, wherein one or more characters not included within said set of data are additionally stored within said digit list file.

4. The system ofclaim 2, wherein said data processing subsystem is further configured to use said digit list file to convert said set of data to said higher base of representation.

5. The system ofclaim 1, wherein said higher base of representation comprises a maximum power of said original base of representation that is less than or equal to 2ⁿ, wherein n is equal to a length of said fixed-length encoding scheme.

6. The system ofclaim 1, further comprising a compression module configured to compress said encoded data.

7. The system ofclaim 1, further comprising a decoder configured to decode said encoded data.

8. The system ofclaim 1, wherein said data processing system is further configured to convert said base-converted data to said original base of representation.

9. The system ofclaim 1, wherein said fixed-length encoding scheme comprises at least one of an American Standard Code for Information Interchange (ASCII) encoding scheme, an Extended Binary-Coded Decimal Interchange Code (EBCDIC) encoding scheme, and a Unicode encoding scheme.

10. The system ofclaim 1, wherein said set of data comprises decimal data.

11. The system ofclaim 1, wherein said set of data comprises a text file.

12. A method comprising:

identifying a total number of unique characters within a set of data, said set of data having an original base of representation equal to said total number of unique characters;

converting said set of data to a higher base of representation, said higher base of representation being greater in value than said original base of representation; and

encoding said base-converted data with a fixed-length encoding scheme.

13. The method ofclaim 12, further comprising storing within a digit list file said unique characters.

14. The method ofclaim 13, further comprising storing within said digit list file one or more characters not included within said set of data.

15. The method ofclaim 13, further comprising using said digit list file to convert said set of data to said higher base of representation.

16. The method ofclaim 12, wherein said higher base of representation comprises a maximum power of said original base of representation that is less than or equal to 2ⁿ, wherein n is equal to a length of said fixed-length encoding scheme.

17. The method ofclaim 12, further comprising compressing said encoded data.

18. The method ofclaim 12, further comprising decoding said encoded data.

19. The method ofclaim 12, further comprising converting said base-converted data to said original base of representation.

20. The method ofclaim 12, wherein said fixed-length encoding scheme comprises at least one of an American Standard Code for Information Interchange (ASCII) encoding scheme, an Extended Binary-Coded Decimal Interchange Code (EBCDIC) encoding scheme, and a Unicode encoding scheme.

21-25. (canceled)

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